Some modest Yahtzee goals

If the probability of getting at least one pair of matching dice when rolling five 6-sided dice is $\frac{a}{b}$, where $a$ and $b$ are positive co-prime integers, then what is $a+b$?

Note: Three-of-a-kind, four-of-a-kind, full house, yahtzee, or two pairs would all count as "at least one pair of matching dice." However, a straight ($\{1,2,3,4,5\}$ or $\{2,3,4,5,6\}$) or a small straight would not count.

Check out The anti-Yahtzee first to make finding the solution to this problem trivial.